Method for Allocation of Communication Parameters in a Multiuser Wireless Communications System

ABSTRACT

A method ( 400 ) for use in a wireless communications system, with a first transmitter ( 410 ) and ( 415 ) a first and a second user, and at least ( 420 ) first and second channels for the first transmitter to transmit to said two users on, which method uses a first Lagrange parameter λ. The method comprises: Defining ( 425 ) a parameter q ij , which represents the inverse channel quality for user u i , and channel j, Finding ( 430 ) all channels for user u i , such that q ij ≦λ i , but q ij ′&gt;λ, V i ′≠i, and designate those channels to user u, If more than one user u, with q i ,  j &lt;λ for a channel j is found, then assign ( 435 ) that channel to the user u i , that ensures the condition q ij /q I′j , &gt;λ i /λ i ′, Vi′≠i. If q ij &gt;λ i , Vi then ( 430 ) leave channel j unassigned Power levels and rates may also be allocated with the aid of the invention.

TECHNICAL FIELD

The present invention discloses a method and a device for allocation ofcommunication parameters in a communications system comprising one ormore sets of one transmitter with multiple users, i.e. receivers, and atleast one channel.

BACKGROUND

In transmitters in wireless communications systems, such as thetransmitters in the base stations of cellular access systems, it is adesire to keep the power consumption low and to maintain energyefficient communication with the users in the cell or cells that is/areserviced by the base station. There are a number of reasons for this,among which the following can be mentioned:

-   -   An operator who can reduce the power/energy consumption will        become more cost-efficient, and thus yield increased revenue.        The energy cost is generally considered to be a substantial part        of the Operating cost.    -   An operator may also be interested in offering the best (or, for        the service, sufficient) performance to his customers in        relation to the power/energy that is invested.    -   Manufacturers are interested in reducing the power/energy        consumption of base stations and other equipment, since that may        lead to lower manufacturing costs due to fewer/smaller cooling        components and power amplifiers, and will improve their        competitiveness and sales margins due to lower manufacturing        costs.    -   Reduced energy/power consumption is also beneficial for solar        panel driven base stations as it enables prolonged operation        and/or increased range given an energy/power budget. This is of        particular interest when enabling cellular services to future        users, who often live in rural areas with little or no        infrastructure, such as an electricity grid.    -   An operator operating a system in remote areas which often lack        distribution systems for electricity may often need to rely on        fuel, e.g. often diesel, driven generators, and hence requires        tedious and costly transport and management of this fuel. It        would be desirable to reduce this problem by a more energy and        power efficient design.    -   More resource-efficient methods for communication are also of        interest for society as a whole, given the climate change        problem, and acknowledging that the source of electricity for        most cellular systems is often based on non-renewable fossil        fuel.

In addition, it is a generally good design philosophy to minimize energyconsumption.

The so called “Water-filling” solution is a well known technique forpower and rate allocation in a cellular wireless access system, whencommunicating over multiple carriers/channels with different gain tonoise ratios, and provides the optimal performance, typically measuredas the sum rate, for a given investment of sum power. The “waterfilling” solution provides power and rate allocation for each channel.

Consider a Gaussian vector channel with J orthogonal channels, eachindexed with the letter j, where the noise-to-gain ratios q_(j)=σ_(j)²/G_(j) are known for all channels, and where σ_(j) ² is the noise andinterference power and G_(j) is the channel gain. The problem is todetermine the channel power allocations P_(j) that maximizes the total(Shannon) rate over all channels subject to a constraint on total sumpower P^((tot)):

$\max {\sum\limits_{\forall j}R_{j}}$${s.t.{\sum\limits_{\forall j}P_{j}}} = P^{({tot})}$R_(j) = log₂(1 + P_(j)G_(j)/σ_(j)²) P_(j) ≥ 0

The term “s.t.” in the equation above stands for “subject to”, andindicates the constraint under which the optimization is performed. Inthis case, the optimization is a maximization of the sum rate for eachchannel j. R_(j) stands for the maximum permissible communication rate.The rate here is synonymous with channel capacity in b/Hz/s.

P_(j)*,R_(j)* are the solutions to the above optimization problemaccording to

$P_{j}^{*} = \left\{ {{\begin{matrix}{{\lambda - {\sigma_{j}^{2}/G_{j}}},} & {{{if}\mspace{14mu} \lambda} > {\sigma_{j}^{2}/G_{j}}} \\{0,} & {Otherwise}\end{matrix}R_{j}^{*}} = {\log_{2}\left( {1 + {P_{j}^{*}{G_{j}/\sigma_{j}^{2}}}} \right)}} \right.$

where λ is a so called Lagrange parameter which is tuned to fulfil thecondition that all the transmit powers add up to a total power P_(tot).

In wireless communications systems, such as cellular access systems, thetransmitter, for example in a base station, generally has the task ofassigning resources, such as channels and rates, for communication withusers of the system, as well as assigning suitable power and rates.

Since a base station may communicate with multiple users, especially inmulticarrier systems such as OFDMA systems exemplified by LTE (i.e.3GPP's Long Term Evolution), IEEE 802.16 and others, the classicalwater-filling solution is interesting, but is insufficient since it doesnot address the existence of multiple users. Other examples of multicarrier systems are SC-FDMA systems. (SC-FDMA: Single Carrier FrequencyDivision Multiple Access).

Commonly in wireless access systems, channel assignment is treatedseparately from power and rate control, i.e. the system first selectschannels, and then, independently, assigns power and rates. Moreover,while there are examples where power and rate are jointly adapted, it iscommon in practice that the system either roughly tries to use a fixedpower level with adaptive rate (HSDPA in 3GPP's WCDMA) or fixed ratewith adaptive power (DCH for WCDMA in 3GPP's WCDMA, or DCH in GSM).

Nevertheless, the problem of dealing with multiple users and assigningpowers and rates simultaneously has been addressed in various forms.However, in general, existing solutions do not provide for a simple, anda flexible framework which is adaptive to different and/or changingpower and rate constraints, both on a system and individual user level.

SUMMARY

Thus, as has been explained above, in a wireless communications systemsuch as a cellular wireless access system, there is a need to find amore structured way than hitherto known to solve the problem of lettinga transmitter, such as a transmitter in a base station, select users andwhich channels they should communicate on, as well as the output powerand rates that should be used.

In addition, there is a need for a method by means of which it would bepossible to jointly determine channel allocation, power and rates for asingle transmitter to multiple users in a multi-channel system wherechannels offer different communication qualities.

These needs are addressed by the present invention in that it disclosesa method for use in a wireless communications system, such as a cellularwireless access system, in which there is at least a first transmitterand at least a first and a second receiver, i.e. users that areassociated with the first transmitter, and at least a first and a secondchannel for said at least first transmitter to transmit to said at leasttwo users on.

The method of the invention uses at least a first Lagrange parameter λ,and the method comprises the following:

-   -   Define a parameter q_(i,j), which represents the inverse channel        quality for user u_(i) and channel j,    -   Find all channels for user u_(i) such that q_(i,j)≦λ_(i) but        q_(i′,j)>λ_(i′), ∀i′≠i, and designate those channels to user        u_(i).    -   If more than one user u_(i) with q_(i,j)≦λ_(i) for a channel j        is found, then assign that channel to the user u_(i) that        ensures q_(i,j)/q_(i′,j)>λ_(i)/λ_(i′), ∀i′≠i.    -   If q_(i,j)>λ_(i), ∀i, channel j is left unassigned.

Suitably, according to the method of the invention, the inverse channelquality parameter q_(i,j) for user u_(i) and channel j is defined asq_(i,j)=σ_(i,j) ²/G_(i,j), where G_(i,j) is the channel gain and thereceiver noise and interference power in the receiver is σ_(i,j) ².

Thus, as will become even more evident from the following detaileddescription of the invention, the present invention offers a flexible,low complexity optimization framework for jointly determininguser-specific channel allocations to the different users in the system,as well as output power and rates, based on Lagrange parameters and onchannel qualities, with a specific, Lagrange based, channel allocationcriteria

In addition, the present invention also offers joint multi-useropportunistic channel dependent scheduling and “water-filling, with thepossibility to efficiently exploit time or frequency fluctuating channelqualities due to fading or varying interference situation

In addition, the present invention further enables the mixing of userindividual sum-power and sum-rate constraints, while optimizing a commonobjective function for all users.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be described in more detail in the following, withreference to the appended drawings, in which

FIG. 1 shows a basic method of the invention, and

FIG. 2 shows a version of the method of FIG. 1, and

FIG. 3 shows a graphic representation of the invention, and

FIG. 4 shows a basic flow chart of a method of the invention, and

FIG. 5 shows a schematic block diagram of a transmitter of theinvention.

DETAILED DESCRIPTION

The present invention will now be described in more detail below, withsome algorithms being shown. It should be noted that although thepresent invention is derived in a heuristic manner, it has a trueoptimization foundation as it to some extent takes the classical“water-filling solution” as its starting point. The “water-fillingsolution” and an exact solution approach are described in detail at theend of this text, for those readers who seek specific details on thosemethods.

As mentioned previously, the present invention is aimed at anapplication in a wireless communications system, where the problem is toallocate channels, output power and rates in communication from asending party such as a base station to a receiving party such as a userwith a mobile terminal in the system.

Assume the following:

-   -   1 transmitter,    -   I≧2 receivers, e.g. users of the system, and    -   J≧2 channels,        where:    -   Each channel for user u_(i) is characterized by its channel gain        G_(i,j), and the corresponding receiver noise and interference        is σ² _(i,j). For brevity, define q_(i,j)=σ_(i,j)/G_(i,j), where        q_(i,j) represents the inverse channel quality for user u_(i)        and channel j.

The problem is now to determine the channel allocation, which is done inthe following manner:

-   -   Channel allocation        -   For each user u_(i), the set of channels to be used, if any,            are determined.        -   The set of channels to be unused, if any, are determined.        -   The determination is based on q_(i,j)s and a set of Lagrange            parameters λ_(i)s, where each λ_(i) may potentially be user            u_(i) specific, see details below.

Specifically, the channel allocation rule proposed by the presentinvention is as follows:

-   -   Find all channels for user u; such that q_(i,j)≦λ_(i), but        q_(i′,j)>λ_(i′), ∀i′≠i, and designate the set of channels to        user u_(i).    -   In the event that there are multiple user u_(i) with        q_(i,j)≦λ_(i) for a channel J, assign the user u_(i) that        ensures q_(i,j)/q_(i′,j)>λ_(i)/λ_(i′), ∀i′≠i.    -   In the event that q_(i,j)>λ_(i), ∀i, channel j is left        unassigned.

The invention may also be used for power and rate allocation in thefollowing manner:

-   -   Power allocation:        -   For each user u_(i) and the selected set of channels to be            used, if any, the power allocation is determined based on            the “water-filling” solution, that is, the determination is            based on q_(i,j)s and a set of Lagrange parameters λ_(i)s,            which may potentially be user u_(i) specific.    -   Rate allocation:        -   For each user u_(i) and the selected set of channels to be            used, if any, the rate allocation is determined based on the            “water-filling” solution, that is, the determination is            based on q_(i,j)s and a set of Lagrange parameters λ_(i)s            which may potentially be user u_(i); specific.

In all, the above specifies a specific mapping from a set of Lagrangeparameters for each user (here assembled in a vector λ), a matrix Q withelements q_(i,j) indicative of the inverse channel quality for user iand channel j, a matrix R with elements R_(i,j) indicative of the ratefor user i and channel j, a matrix P with elements P_(i,j) indicative ofthe power for user i and channel j. Only one user may be allocated apower and rate, so the matrices R and P also indicate the how channelsare allocated among users. The mapping is hence f(λ,Q)→{R,P}. In thisformulation, users that are not allocated a channel will have a zerorate and a zero power. At most, and if the channel is not unused, onlyone user is allocated to a channel, and then using non-zero power andnon-zero rate. To complement this description, where the channelallocation is implicit in the matrices R (or P) with the non-zeroelements, and to show more explicitly that users are allocated channels,a channel allocation vector C with the respective user for each channelmay be defined.

An example of a channel allocation vector could take the form c={u₄, u₃,u₉, u₁ . . . , -, u₁, u₉}, which illustrates that each channel isassigned a user u_(i), or is unused, the latter indicated with thesymbol “-”, i.e. a hyphen.

Also note that the interference included in σ² _(i,j) could arise fromany other source, such as one or more similar arrangements of theinvention, i.e. one or more sets with a sender that is in communicationwith a set of user, wherein the sender assign channels, power levels andrates according to the invention. Whenever, as illustrated below, aniterative determination of channel, power level and rate allocations forthe users is used, the interference level may vary for each iterationround.

A few words can be added regarding the Lagrange parameters: this is aparameter that arises in optimization problems when solved withLagrange's optimization method. The Lagrange parameter is tuned tofulfill some condition under which the optimization is performed.

Returning now to the channel allocation rule of the invention, and thetest of q_(i,j)/q_(i′,j)>λ_(i)/λ_(i′), ∀i′≠i, only the set of users forwhich q_(i,j)≦λ_(i) is valid need to be tested. Also, only the“surviving” user of the test q_(i,j)/q_(i′,j)>λ_(i)/λ_(i′), ∀i′≠i needsto be tested against the next untested user for the considered channel.Hence, the complexity can be kept fairly low.

FIG. 1 shows the overall system architecture of a method 100 of theinvention, and pictorially shows how the method or algorithm 100 may beused to find the optimal user-channel allocation the transmitter outputpower levels and/or rates R_(i,j) based on Lagrange parameter inputsλ_(i) for user u, as described above. The input “101” to the algorithm100 is thus λ_(i) ∀i, and the output 102 is P_(i,j) and R_(i,j); ∀i, j.

FIG. 2 shows another possible version 200 of the method of theinvention, where the same parameters, i.e. P_(i,j), R_(i,j) aredetermined, but now with an iterative approach in order to fulfil thesum optimization problem with a sum rate and/or power constraint or aset of rate and/or power individual constraints.

In more detail, the method 200 illustrated in FIG. 2 comprises analgorithm 210 which is basically the same as the algorithm of FIG. 1,but the method 200 also comprises a λ_(i) calculator 230 for all usersu_(i), which is used in order to find a new set of λ_(i)s, shown as 205in FIG. 2, based on the following input values, as shown by the inputarrows numbered as 201, 202, 203 and 204 in FIG. 2:

-   -   201: a tolerance input T_(j), which measures the deviation from        the calculated performance against the desired performance        constraints for each channel, i.e. T_(j); ∀j.    -   202: the initial values for the Lagrange parameters, i.e. λ_(i)        ^((start)) for each user u_(i), mathematically expressed as        λ_(i) ^((start)); ∀i.    -   203: the sum parameter to optimize, i.e. the sum of all rates or        the sum of all output power levels. Nota bene, only one        parameter, the rate or the power, may be selected as the sum        parameter to be optimized. Mathematically, this can be expressed        as:

$\min {\sum\limits_{\forall j}{\sum\limits_{\forall i}P_{i,j}}}$or  ∀i, j$\max {\sum\limits_{\forall j}{\sum\limits_{\forall i}R_{i,j}}}$

-   -   204: the sum rate and/or power constraint P^((tot)) and        R^((tot)), or an individual per user power and/or rate        constraints, P_(i) ^((tot)) and R_(i) ^((tot)), which        mathematically can be expressed as:    -   P^((tot)) or R^((tot)); ∀i    -   or    -   P_(i) ^((tot)) and/or R_(i) ^((tot)); ∀i    -   the estimated performance values from the previous iteration        round,

The output 205 of the algorithm block 210 can also be expressed as λ_(i)^((n)); ∀i.

Based on the set of λ_(i)s, the algorithm block 210 determines the(n+1)^(th) iteration of transmitter output power level, the rate anduser-channel allocations, shown as the output 206 P_(i,j) ^((n+1)),R_(i,j) ^((n+1)) from the algorithm block. The output 206 can also beexpressed mathematically as:

${P_{i,j}^{({n + 1})}\mspace{14mu} {and}\mspace{14mu} R_{i,j}^{({n + 1})}\; {\forall i}},{j\begin{pmatrix}{if} & {P_{i,j}^{({n + 1})} \neq {0\mspace{14mu} {then}}} & {{{P_{i^{\prime},j}^{({n + 1})} \neq 0}\;,{\forall{i^{\prime} \neq i}}}\mspace{11mu}} & {and} \\\; & {R_{i,j}^{({n + 1})} \neq {0\mspace{14mu} {then}}} & {{{R_{i^{\prime},j}^{({n + 1})} \neq 0}\;,{\forall{i^{\prime} \neq i}}}\;} & \;\end{pmatrix}}$

The method 200 also comprises a performance calculator 220,“Performance”, which uses the output values P_(i,j) ^((n+1)), R_(i,j)^((n+1)) from the algorithm 210 in order to estimate the sum performancefor all users, as well as relevant performance measures that relate tosum rate and/or power constraint, or the individual per user powerand/or rate constraints. The performance measure is determined based onthe sum maximization input to the λ_(i) calculator. If the sum power(i.e. the sum over all users and channels) is to be optimized, then thesum power is used as the performance measure, and likewise for the rate.

The Lagrange parameters λ_(i) maybe determined within the scope of thepresent invention using various strategies, which enable differentoptimization objectives to be achieved. Examples of such strategies aregiven below:

-   -   Different and independent λ_(i)s may be used, in order to fulfil        independent per user link optimization with per user link        constraints. This can for example solve the problem

$\max {\sum\limits_{\forall j}R_{i,j}}$${s.t.{\sum\limits_{\forall j}P_{i,j}}} = P_{i}^{({tot})}$

-   -   or the problem

$\min {\sum\limits_{\forall j}P_{i,j}}$${s.t.{\sum\limits_{\forall j}R_{i,j}}} = R_{i}^{({tot})}$

-   -   Coupled λ_(i)s may be used, in order to fulfil interdependent        system optimization with system or per user link constraints,        with the following sub cases:        -   Identical λ_(i)s are used, which implies system constraints.            This can solve the problem:

$\max {\sum\limits_{\forall j}{\sum\limits_{\forall i}R_{i,j}}}$${s.t.{\sum\limits_{\forall j}{\sum\limits_{\forall i}P_{i,j}}}} = P^{({tot})}$

-   -   or the problem

$\max {\sum\limits_{\forall j}{\sum\limits_{\forall i}P_{i,j}}}$${s.t.{\sum\limits_{\forall j}{\sum\limits_{\forall i}R_{i,j}}}} = R^{({tot})}$

-   -   -   Proportional scaling of λ_(i)s may be used, i.e. λ_(i)s is            used, i.e. λ_(i)=xλ_(i) ⁰, λ_(i)=xλ_(i′) ⁰, where λ_(i)            ⁰≠λ_(i′) ⁰ is allowed, and where λ_(i) ⁰=E{q_(i,j)}. This            enables opportunistic (channel dependent) scheduling in            fading channels that also incorporate power and rate            allocation through water-filling. From an opportunistic            scheduling point of view, using λ_(i) ⁰=E{q_(i,j)} is            equivalent to a proportionally fair scheduler criterion            according to

$\hat{i} = {\arg {\max\limits_{\forall i}\left\{ {q_{i,j}/{\overset{\_}{q}}_{i,j}} \right\}}}$

The above operations, with the various constraints implied, may furtherbe supplemented with means for adapting the Lagrange parameters, suchthat:

-   -   Constraints are fulfilled, including:        -   Power and rate constraints        -   Sum (i.e. over all users) and per users constraints

Note that when a rate based optimization is performed, one shouldmaximize the measure, whereas for the power based optimization, thepower is minimized.

The method of the invention can also be shown by means of a graphicvisualization, which is shown in the graph 300 FIG. 3. FIG. 3 shows atwo-user case with six channels C₁ to C₆. The vertical and thehorizontal axes show the inverse quality for user one, q₁, and two, q₂,respectively. Each of the six channels is shown in the graph as a cross,and dotted lines represent the Lagrange parameters λ₁ and λ₂ for therespective user u₁ and u₂. The lines represented by the Lagrangeparameters λ₁, λ₂ may be seen as delineating respective “allocationareas” for the channels C₁ to C₆ in the graph, with the channelassignments being shown by means of straight lines from the cross whichrepresents a channel to one of the Lagrange parameters λ₁ or λ₂. As canbe seen, channel 2, i.e. C₂, is not assigned to either of the two usersin the example, since that channel is not inside either of theallocation areas. The term “not inside”, as can be realized from FIG. 3,means that channel 2 does not have a q_(i) value which is lower thaneither of the Lagrange parameters λ₁ or λ₂.

As can also be seen from the graph in FIG. 3, channels 1, 4, and 6 areassigned to user 1, since they are inside the allocation area defined byλ₁, and channels 3 and 5 are assigned to user 2.

FIG. 3 also shows a line from the origin, i.e. (0, 0), to the crossingpoint between the lines of the two Lagrange parameters λ₁ and λ₂. Thisline from (0, 0)→(λ₁, λ₂) is the border between the two user allocationregions. As can also be seen, there is a potential “conflict area” forchannels which are inside the allocation areas of both users, i.e.channels which are below the line defined by λ₁ but also to the left ofthe line defined by λ₂. Allocation conflicts, such as those in the caseof channels 3 and 6 of FIG. 3 are resolved using the rule ofq_(i,j)/q_(i′,j)>λ_(i)/λ_(i′), ∀i′≠i. As an example of how this rule isapplied, take channel 3, i.e. C₃:

q _(1,3) /q _(2,3)>λ₁/λ₂

Channel 3 is thus allocated to user 2, which is shown by means of astraight line from the cross of channel 3 to λ₂. In a similar manner,channel 6 is allocated to user 1, λ₁. The rule which was used forallocating channel inside the “conflict area” can also be seen asfollows: a line may be imagined form the origin (0,0) to the cross whichindicates the channel. If the slope of this line is steeper than theslope of the line from the origin to the cross of λ₁/λ₂, the channelwill be allocated to user 1, λ₁, otherwise the channel will be allocatedto user 2, λ₂.

The line from the cross of a channel to the Lagrange line, whichindicates the channel which user is allocated to, may also be seen as anindicator of the output power to be used for that channel to that user.Thus, for example, the line from channel 5 is shown as P₂ ⁵, whichindicates not only that channel 5 will be used for user 2, but thelength of the arrow also indicates the output power that may be used forchannel 5.

Writing out the channel allocation vector for FIG. 3 gives c={u₁, -, u₂,u₁, u₂, u₁}.

The graph 300 of FIG. 3 only shows a two user case, which is for reasonsof clarity and ease of explanation and the reader's understanding of theinvention, but the method can be straightforwardly extended to anyI-user case, where I≧2.

With continued reference to FIG. 3, a few aspects on optimization andwhat is optimized will now be discussed.

-   -   When different and independent λ_(i)s are used, one realizes        that if no channels are situated in an allocation region common        to multiple users, the optimization will be per user, and the        constraint is per user. However, for any channel that resides in        an allocation region common to multiple users, it is not        immediately evident which user that channel should be allocated        to. Yet, as soon as a channel is allocated to any one user,        classical single user water-filling gives the optimal power and        rate allocation. In choosing one user, among multiple users, for        the channel, one connects the optimization parameter and gets a        common function.    -   When coupled and identical λ_(i)s are used, it can be seen that        the optimization is system oriented, i.e. over all users and        channels, and with a system related constraint. The bordering        line between user allocation areas represents the same rate        allocation for a channel, lying on the line, regardless of which        user it is allocated to. Hence, the condition        q_(i,j)/q_(i′,j)>λ_(i)/λ_(i′), ∀i′≠i ensures that a channel will        be allocated to the user which uses the least power.

The invention also allows for a mixture of power and rate constraints,apart from having a sum power or a sum rate constraint (over all usersand channels), i.e. one user may have a rate constraint, whereas anotheruser has a power constraint. The constraint should be seen as the sum ofpower (or rate) that a user should achieve over all its assignedchannels.

FIG. 4 shows a schematic flowchart 400 of a method of the invention.Steps which are options or alternatives are shown with dashed lines. Asindicated in step 410 of FIG. 4, the method comprises using at least afirst transmitter, and as shown in step 415, at least a first and asecond receiver, i.e. users, and at least, step 420, a first and asecond channel for said at least first transmitter to transmit to saidat least two users on.

As described previously in this text, the method 400 uses at least afirst Lagrange parameter λ per user, as shown in step 422, and comprisesthe following:

-   -   Define, step 425, a parameter q_(i,j), which represents the        inverse channel quality for user u_(i) and channel j,    -   Find, step 430, all channels for user u_(i) such that        q_(i,j)≦λ_(i) but q_(i′,j)>λ_(i′), ∀i′≠i, and designate those        channels to user u_(i).    -   If more than one user u_(i) with q_(i,j)≦λ_(i) for a channel j        is found, then assign, step 435, that channel to the user u,        that ensures the condition q_(i,j)/q_(i′,j)>λ_(i)/λ_(i′), ∀i′≠i.    -   If q_(i,j)>λ_(i), ∀i, then, step 440, leave channel j        unassigned.

As is indicated in step 450, the inverse channel quality parameterq_(i,j) for user u_(i) and channel j is defined as q_(i,j)=σ²_(i,j)/G_(i,j), where G_(i,j) is the channel gain and the receiver noiseand interference power in the receiver is σ² _(i,j).

As shown in steps 445 and 455, the output power(s) P and rate(s) R forthe first transmitter to said first u₁ and second u₂ receivers onchannel j is also determined using q_(i,j) and a set of Lagrangeparameters λ_(i).

FIG. 5 shows a rough block diagram of a transmitter 500 according to thepresent invention. As indicated in FIG. 5, the transmitter 500 maycomprise an antenna 510, or means for being connected to such anantenna. In addition, the transmitter 500 will comprise transmit means,Tx 530, as well as a control function or control means, suitably amicrocomputer 520 or some other form of processor.

The control means 520 will serve to control the transmitter 500 in thevarious ways described above and shown in FIGS. 1-4.

The transmitter of the invention, as described above, and as exemplifiedby the transmitter of FIG. 5, may be a transmitter in more or less anywireless communications system. However, applications which may bementioned are transmitters in base stations in cellular communicationssystems, such as for example, OFDMA systems, as exemplified by LTE (i.e.3GPP′s Long Term Evolution) and IEEE 802.16. Other examples of cellularsystems in which the invention may be applied are SC-FDMA systems.(SC-FDMA: Single Carrier Frequency Division Multiple Access)

The invention is not limited to the examples of embodiments describedabove and shown in the drawings, but may be freely varied within thescope of the appended claims.

Also, in the following, some of the mathematical background to theinvention will be given.

Single User Power Allocation on a Gaussian Vector Channel

This section contains, for reference, a derivation of the so calledwater-filling solution to the (single-user) power allocation problem.The derivation is not required for the invention, but serves toillustrate the origin of “water levels” in the context of powerallocation in communication networks.

Consider a Gaussian vector channel with J orthogonal channels where thenoise-to-gain ratios q_(j)=σ_(j) ²/G_(j) are known for all channels. Theproblem is to determine the channel power allocations P_(j) thatmaximizes the total Shannon rate over all channels subject to aconstraint on the total sum power P^((tot)):

(P-SU):$\max {\sum\limits_{j = 1}^{J}\; {\log \left( {1 + \frac{P_{j}}{q_{j}}} \right)}}$${s.t.{\sum\limits_{j = 1}^{J}\; P_{j}}} \leq P^{({tot})}$P_(j) ≥ 0   j = 1, K, J

P-SU is a convex non-linear programming (NLP) problem since it is amaximization problem with a concave objective function (sum of concavefunctions) and convex constraints. The feasible set clearly alsocontains interior points (when P^((tot))>0) so Slater's constraintqualification condition is fulfilled. Hence, the first-order KKT(Karush-Kuhn-Tucker) conditions are necessary and sufficient foroptimality.

Now, form the Lagrangian:

${L\left( {{P.\lambda},\mu} \right)} = {{\sum\limits_{j = 1}^{J}\; {\log_{2}\left( {1 + {P_{j}/q_{j}}} \right)}} - {\lambda\left( {{\sum\limits_{j = 1}^{J}\; P_{j}} - P_{tot}} \right)} + {\sum\limits_{j = 1}^{J}\; {\mu_{j}{P_{j}.}}}}$

The KKT conditions can be stated as:

$\begin{matrix}{{\left( {\nabla_{p}{L\left( {\overset{\_}{P},\overset{\_}{\lambda},\overset{\_}{\mu}} \right)}} \right)_{j} = {{\frac{1/q_{j}}{1 + {{\overset{\_}{P}}_{j}/q_{j}}} - \overset{\_}{\lambda} + {\overset{\_}{\mu}}_{j}} = 0}},{j = 1},K,J,} & (i) \\{\overset{\_}{\lambda},{\overset{\_}{\mu} \geq 0},} & ({ii}) \\{{{\overset{\_}{\lambda}\left( {{\sum\limits_{j = 1}^{J}\; {\overset{\_}{P}}_{j}} - P_{tot}} \right)} = 0},} & ({iii}) \\{\overset{\_}{\mu},{{\overset{\_}{P}}_{j} = 0},{j = 1},K,{J.}} & ({iv})\end{matrix}$

In addition the primal feasibility constraints need to be satisfied:

$\begin{matrix}{{{\sum\limits_{j = 1}^{m}\; {\overset{\_}{P}}_{j}} \leq P_{tot}},} & (v) \\{{{\overset{\_}{P}}_{j} \geq 0},{j = {1.{K.J.}}}} & ({vi})\end{matrix}$

Assume first Σ_(j=1) ^(J) P _(j)<P_(tot). Then (iii) gives λ=0 and (i)yields 1=− μ _(j)( P _(j)+q_(j)), which is infeasible since P _(j)≧0, μ_(j)≧0 by (ii) and (vi), and q_(j)>0. Hence Σ_(j=1) ^(J) P _(j)=P_(tot)and λ>0. Next, assume P _(j)>0. Then μ _(j)=0 by (iv) so (i) gives us 1=λ( P _(j)+q_(j)), which after substitution of λ′=1/ λ gives:

P _(j) = λ′−q _(j).

That is, if power is allocated to channel j then it should be equal tothe difference between a certain “water”-level λ′=1/ λ minus thenoise-to-gain value for this channel. The value of the “water”-level λ′can be derived from the equality required in (v):

${{\sum\limits_{j = 1}^{J}\; {\overset{\_}{P}}_{j}} = {{{\sum\limits_{j\text{:}\overset{\_}{J}}\; {\overset{\_}{\lambda}}^{\prime}} - q_{j}} = {{{\overset{\_}{\lambda}{\overset{\_}{J}}} - {\sum\limits_{j\text{:}\overset{\_}{J}}\; q_{j}}} = P_{tot}}}},$

where J={j: P ^(j)>0} is the set of channels with positive powerallocated. Reshuffling yields:

${\overset{\_}{\lambda}}^{\prime} = {\frac{P_{tot} + {\sum\limits_{j\text{:}\overset{\_}{J}}\; q_{j}}}{\overset{\_}{J}}.}$

Since P _(j)= λ′−q_(j), a channel j can be given positive power P _(j)>0if and only if all channels ĵ with q_(j)<q_(j) have been given positivepower P _(ĵ)>0. This observation leads to the following scheme todetermine λ′:

-   -   1. Sort the channels in increasing values of q_(j).    -   2. Add the first channel to J, compute λ′.    -   3. Try to add the next channel ĵ to J, compute updated λ′.    -   4. If λ′>q_(j) then keep ĵ in J and go to 3, otherwise stop.

The output power levels are then finally allocated as P _(j)= λ−q_(j)for ĵ in J.

Exact Solution Approaches to the Multi-User Joint Channel, Power andRate Allocation Problem

The general multi-user joint channel, power and rate allocation problemwith individual rate and power constraints, i.e. the problem addressedby the present invention, can be posed as the following optimizationproblem:

(P-MU):$\max {\sum\limits_{i = 1}^{I}\; {\sum\limits_{j = 1}^{J}\; {x_{i,j}{\log \left( {1 + {P_{i,j}/q_{i,j}}} \right)}}}}$${s.t.{\sum\limits_{i = 1}^{I}\; {\sum\limits_{j = 1}^{J}\; P_{i,j}}}} \leq P_{tot}$$\begin{matrix}{{\sum\limits_{j = 1}^{J}\; {\log \left( {1 + {P_{i,j}/q_{i,j}}} \right)}} \geq R_{i,\min}} & {\forall{i \in I^{R}}} \\{{\sum\limits_{j = 1}^{J}\; P_{i,j}} \leq P_{i,\max}} & {\forall{i \in I^{P}}} \\{{\sum\limits_{i = 1}^{J}\; x_{i,j}} \leq 1} & {\forall j} \\{P_{i,j} \geq 0} & {{\forall i},{\forall j}} \\{x_{i,j} \in \left\{ {0,1} \right\}} & {{\forall i},{\forall j}}\end{matrix}$

As above the J channels are orthogonal and the noise-to-gain ratiosq_(i,j)=σ_(i,j) ²/G_(i,j) are known for all combinations of channels andthe I users. The binary variables x_(i,j) indicate if channel j is usedfor user i (x_(i,j)=1) or not (x_(i,j)=0) whereas the continuousvariables P_(i,j) is the power allocated to channel j for user i. Thefirst constraint limits the total sum power to P_(tot), the second andthird are user-individual rate and power constraints for some subsets ofusers I^(R), I^(P), and the fourth constraint states that at most oneuser can be allocated to a given channel. The problem is to determine xand P such that the total Shannon rate over all channels is maximized.

P-MU is an integer nonlinear programming (I-NLP) problem, and is relatedto the single-user power allocation problem for which the optimalsolution is known and can be computed very efficiently, as shown aboveunder the heading “Single user power allocation on a Gaussian vectorchannel”.

If the individual power and rate constraints are removed, it isstraightforward to find the structure of the optimal solution. Supposepower is allocated to a channel for a particular user in a givenfeasible solution, and another user has a lower q_(i,j) on this channel,then an improved feasible solution can be obtained by simply reassigningthe channel to the other user using the same power. Hence, a strategy tosolve P-MU is to first assign channels to users in a “greedy” fashion,i.e. with minimal q_(i,j) for all I, as described by the invention, andto then apply “water-filling” on the resulting set of power variables.

The “greedy” solution strategy described above does not work in generalfor P-MU. One tool for devising practical algorithms for the generalP-MU is to analyze it using exact optimization algorithms. These exactalgorithms are likely not of interest in practice for the problem, butmay serve as guidelines for practical schemes and can give bounds onperformance.

Exact algorithms for integer programs are often based on so called“branch-and-bound” schemes. To demonstrate the structure of such amethod, it is applied to the P-MU problem without the individual rateand power constraints, in spite of the “greedy” method described above.

First note that if the fourth (logic) constraint is removed from P-MU,and all the binary variables are set to one, then the remaining problemcan be seen as a single-user power allocation problem on an I·J vectorchannel. The solution to this “relaxed” problem is easily found usingthe “water-filling” scheme described above. However, the solution may beinfeasible for P-MU, that is, it violates the removed constraint, andallocates power to multiple users on the same channel.

A feasible solution and a lower bound can be created from eachinfeasible solution by a “greedy” heuristic solution, where the userthat was given the highest rate on a particular channel takes over allpower assigned to that channel, while still respecting the total powerlimitation. Branching can be done on the entire logic constraint, sinceit is a so called special ordered set of type 1, instead of individualbinary variables, and may be limited to the most “promising” variables,e.g. highest rates, in an infeasible solution.

For the general P-MU case with individual rate and/or power constraints,the same approach can be applied. The relaxation problems are then nolonger simple “water-filling” problems, but can be solved either byusing a general solver for non-linear problems or by “water-filling”strategies for constrained power allocation problems.

1-30. (canceled)
 31. A method for use in a wireless communicationssystem in which there is at least a first transmitter and at least afirst and a second receiver as at least two users, and at least a firstand a second channel for said at least first transmitter to transmit tosaid at least two users on, wherein the method uses at least twoparameters lambda_i (λ_(i)), and comprises: defining a parameter q_(i,j)which represents the inverse channel quality for user u_(i) and channelj; setting lambda_i (λ_(i)) to be proportional to q_i, i.e.,λ_(i)=x_i*E(q_i), where x_i is a fixed or slowly changing parameter foruser i; finding all channels for user u_(i) such that q_(i,j)≦λ_(i) butq_(i′,j)>λ_(i′), ∀i′≠i, and designating those channels to user u_(i); ifmore than one user u_(i) with q_(i,j)≦λ_(i) for a channel j is found,then assigning that channel to the user u_(i) that ensures the conditionq_(i,j)/q_(i′,j)>λ_(i)/λ_(i′), ∀i′≠i; and if q_(i,j)>λ_(i), ∀i, thenleaving channel j unassigned.
 32. The method of claim 31, according towhich the inverse channel quality parameter q_(i,j) for user u_(i) andchannel j is defined as q_(i,j)=σ_(i,j) ²/G_(i,j), where G_(i,j) is thechannel gain and the receiver noise and interference power in thereceiver is σ_(i,j) ².
 33. The method of claim 31, according to whichthe output power for the first transmitter to one of said first u₁ andsecond u₂ receivers on channel j is also determined, using q_(i,j) and aset of Lagrange parameters λ_(i).
 34. The method of claim 33, accordingto which, for channel j and the user i of that channel, the power levelP_(i,j) is chosen as P_(i,j)=λ_(i)−q_(i,j).
 35. The method of claim 34,according to which the set of Lagrange parameters is user specific foruser u_(i).
 36. The method of claim 31, according to which the rate forthe first transmitter to one of said first u₁ and second u₂ receivers onchannel j is also determined, using q_(i,j) and a set of Lagrangeparameters λ_(i).
 37. The method of claim 36, according to which therate for the transmitter to a user i on channel j is determined aslog₂(1+p_(i,j)/q_(i,j))
 38. A transmitter for use in a wirelesscommunications system in which there is at least a first and a secondreceiver as at least two users, said transmitter being configured fortransmitting on at least a first and a second channel to transmit tosaid at least two users on, and said transmitter including a controlcircuit configured for using at least two parameters lambda_i (λ_(i))and further configured to: define a parameter q_(i,j), which representsthe inverse channel quality for user u_(i) and channel j; set lambda_ito be proportional to q_i, i.e., λ_(i)=x_i*E(q_i), where x_i is a fixedor slowly changing parameter for user i; finding all channels for useru_(i) such that q_(i,j)≦λ_(i) but q_(i′,j)>λ_(i′), ∀i′≠i, anddesignating those channels to user u_(i); if more than one user u_(i)with q_(i,j)≦λ_(i) for a channel j is found, then assign that channel tothe user u_(i), which ensures the conditionq_(i,j)/q_(i′,j)>λ_(i)/λ_(i′), ∀i′≠i; and if q_(i,j)>λ_(i), ∀i, leavingchannel j unassigned.
 39. The transmitter of claim 38, in which thecontrol circuit define the inverse channel quality parameter q_(i,j) foruser u_(i) and channel j as q_(i,j)=σ_(i,j) ²/G_(i,j), where G_(i,j) isthe channel gain and the receiver noise and interference power in thereceiver is σ_(i,j) ².
 40. The transmitter of claim 38, in which thecontrol circuit is configured to determine the output power for thefirst transmitter to one of said first u₁ and second u₂ receivers onchannel j using q_(i,j) and a set of Lagrange parameters λ_(i).
 41. Thetransmitter of claim 40, in which the control circuit, for channel j andthe user i of that channel, chooses the power level P_(i,j) asP_(i,j)=λ_(i)−q_(i,j).
 42. The transmitter of claim 40, in which thecontrol circuit is configured to use a set of Lagrange parameters whichis user specific for user u_(i).
 43. The transmitter of claim 38, inwhich control circuit is configured to determine the rate for thetransmitter to one of said first u₁ and second u₂ receivers on channelj, using q_(i,j) and a set of Lagrange parameters λ_(i).
 44. Thetransmitter of claim 43, in which the rate for the transmitter to a useri on channel j is determined by the control circuit aslog₂(1−p_(i,j)/q_(i,j)).